MATHS SPM PAPER 1 QUESTIONS - api.ning.comapi.ning.com/files/4aPiF8TWV1mSnnT4gyjRPWwQAh2Fh5Xhze5CQsUb*B1x4X…3. Each question is followed by four choices of answers A, B, C and D

SULIT 1449/2

1449/1MathematicsPaper 1May20101 ¼ hours

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1449/2© 2010 Hak Cipta JPM [Lihat halaman sebelah

PEPERIKSAAN SELARAS PERTENGAHAN TAHUNSIJIL PELAJARAN MALAYSIA 2010

MATHEMATICS

Paper 1

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO

1. This question paper is bilingual.

2. Answer all questions.

3. Each question is followed by four choices of answers A, B, C and D.

4. For each question, choose one answer only.

5. The diagrams given are not drawn according to scale unless stated.

6. A list of formulae is given on pages 2 and 3.

7. Non programmable scientific calculator is allowed.

This question paper consists of 19 printed pages

The following formulae may be helpful in answering the questions. The symbols given arethe ones commonly used.

RELATIONS

1 nmnm aaa

JABATAN PELAJARAN MELAKA

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2 nmnm aaa

3 mnnm aa )(

4

ac

bd

bcadA

11

5 Sn

AnAP

)()(

6 )(1)'( APAP

7 212

212 )()(Distance yyxx

8 Midpoint,

2,

2),( 2121 yyxx

yx

9 Average speed =takentime

travelleddistance

10 Mean =dataofnumber

dataofsum

11 Mean =sfrequencieofsum

frequency)mark(classofsum

12 Pythagoras Theorem222 bac

1312

12

xx

yym

14 m =intercept

ntercept

x

iy

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SHAPES AND SPACE

1 Area of trapezium =2

1 sum of parallel sides height

2 Circumference of circle = rd 2

3 Area of circle = 2r

4 Curved area of cylinder = hr2

5 Surface area of sphere = 24 r

6 Volume of right prism = cross section length

7 Volume of cylinder = hr 2

8 Volume of cone = hr 2

3

1

9 Volume of sphere = 3

3

4r

10 Volume of right pyramid = 3

1base area height

11 Sum of interior angles of a polygon = (n – 2) 180º

12o360

centreatsubtendedangle

circleofncecircumfere

lengtharc

13o360


circleofarea

sectorofarea

14 Scale factor, k =PA

PA'

15 Area of image = k2 area of object

Answer all questions.

1 Round off 53276 correct to three significant figures.Bundarkan 53276 betul kepada tiga angka bererti.

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A 53000B 53200C 53280D 53300

2 Express 4980000 in standard formUngkapkan 4980000 dalam bentuk piawai

A 4.98 10 − 6

B 4.98 10 − 4

C 4.98 10 4

D 4.98 10 6

3 2.3 10 − 5 − 9.5 10 − 6 =

A 1.35 10 − 5

B 1.35 10 − 6

C 7.2 10 − 5

D 7.2 10 − 6

4 Diagram 1 shows an empty tank, which is a cylinder, with diameter 600 cm andheight 400 cm .Rajah 1 menunjukkan sebuah tangki kosong berbentuk silinder dengan diameter 600 cm danketinggian 400 cm

Diagram 1Rajah 1

A worker fill up 75% of the tank with water.Calculate the volume, in cm3,of water in the tank.Seorang pekerja memasukkan air kedalam tangki itu sehingga 75% penuh.Hitung isipadu,dalam cm3, air dalam tangki itu.

A 8.5 10 − 7

B 8.5 10 7

C 2.83 10 − 7

D 2.83 10 7

5 101012 − 1012 =

A 100002

B 100102

C 101002

D 101102

600 cm

400 cm

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6 Express 3248 as a number in base five.Ungkapkan 3248 sebagai satu nombor dalam asas lima.

A 22445

B 44225

C 13225

D 22315

7 Diagram 2 shows a regular pentagon ABCDE . DEF is a straight line and EA = EFRajah 2 menunjukkan sebuah pentagon sekata ABCDE. DEF ialah garis lurus dan EA = EF.

Diagram 2Rajah 2

The value of x + y isNilai x + y ialah

A 108B 126C 144D 162

8 In Diagram 3, PSR is a tangent to the circle at point S and QT = QS.Dalam Rajah 3 , PSR ialah tangen kepada satu bulatan di titik S dan QT = QS.

A

B

C

DEFxo

yo

52o

y o

R

QP

Diagram 3Rajah 3

S T

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The value of y isNilai y ialah

A 38o

B 52o

C 64o

D 76o

9 Diagram 4 shows five trapezium drawn on square grids .Rajah 4 menunjukkan lima trapezium dilukis pada grid segiempat sama .

Diagram 4Rajah 4

Which of the trapezium A , B , C or D , is an image of trapezium W under atranslation?Antara trapezium A , B , C atau D , yang manakah imej bagi trapezium W di bawah suatu translasi?

10 Diagram 5 shows two parallelograms , P and Q , drawn on a Cartesian plane . Q istheimage of P under an enlargement .Rajah 5 menunjukkan dua segi empat selari , P dan Q, dilukis di atas satah Cartesan. Q ialah imej

bagi Pdi bawah suatu pembesaran .

W

D

A

C

B

y

7

6

5

4

3

2

1

8

9

Q

P

x

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Find the centre of the enlargementCari pusat pembesaran itu .

A ( 10 , 1 )

B ( 5 , 2 )

C ( 2 , 3 )

D ( 1, 5 )

11 Given that tan θ = 2.1445 and 180° ≤ θ ≤ 360o . Find the value of θ.Diberi bahawa tan θ = ─ 2.1445 dan 180o ≤ θ ≤ 360o. Carikan nilai θ.

A 65o

B 115o

C 245o

D 295o

12 In Diagram 6 QRS is a straight line.Dalam Rajah 6 , QRS ialah garis lurus .

What is the value of cos θ ?Apakah nilai kos θ ?

A5

4

S

Diagram 6Rajah 6

θo

Q

P

R

8 cm6 cm

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B5

3

C5

3

D5

4

13 Diagram 7 shows the graphs y = sin x and y = cos x for 180o ≤ x ≤ 360o

Rajah 7 menunjukkan graf y = sin x dan y = kos x untuk 18 00 ≤ x ≤ 3600.

P is an intersection point of the graph y = cos xo and y = sin x . The y-coordinate ofP

is − 0.7071 . Find the value of θ .P ialah titik persilangan bagi graf y = kos xo dan y = sin x. Koordinat-y bagi P ialah – 0.7071 .Cari nilai θ .

A 45B 135C 225D 250

14 Diagram 8 shows a cuboid with horizontal base PQRS. Points L , M and N are themidpoints of UR , TS and UR respectively.Rajah 8 menunjukkan sebuah kuboid dengan tapak PQRS. Titik L , M dan N ialah titik tengah bagiUR, WP dan TS masing-masing.

Diagram 8Rajah 8

Name the angle between plane MRU and plane RSTU.Namakan sudut antara satah MRU dengan satah RSTU.

1

1

360o180o

y

x

Diagram 7Rajah 7

270o

P(θ ,− 0.7071)

T

M

PQ

R

U

S

N WV

L

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A MRSB MRNC MLND MUT

15 Diagram 9 shows two vertical towers, KL and MN, on a horizontal plane. The angleof elevation of vertex M from vertex K is 48°.Rajah 9 menunjukkan dua tiang tegak. KL dan MN pada satah mengufuk. Sudut dongak puncak Mdari puncak K ialah 48o.

Calculate the angle of depression of the base N from the vertex K.Hitung sudut tunduk tapak N dari puncak KA 12° 33´B 23° 25´C 36° 10´D 48° 23´

16 In the Diagram 10, PQ and RS are two vertical pillars standing on horizontal ground.The angle of elevation of Q from S is 22°.Dalam Rajah 10 , PQ dan RS adalah dua tiang tegak berdiri pada permukaan tanah.Sudut dongak titik Q dari titik S ialah 22o

Calculate the value of h.Hitung nilai h

A 3.23B 5.23C 19.83D 21.83

L

K

M

N

8 m

6 m

Diagram 9Rajah 9

Q

P 8 m R

Sh m

2 m

Diagram 10Rajah 10

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17 Which of the following graphs represents the function 42 xy ?

Graf manakah yang mewakili fungsi 42 xy ?

A B

C D

18 Given that x is an integer, find all the values of x that satisfy both of the inequalities

732 x and .536

5x

Diberi x ialah integer,carikan semua nilai-nilai x yang memuaskan kedua-dua ketaksamaan

732 x dan .536

5x

A − 5, − 4 , − 3, − 2 , − 1 , 0 , 1 , 2

B − 5, − 4,− 3, − 2, − 1 , 0 , 1 , 2 , 3

C − 4 ,− 3 , − 2 , − 1 , 0 , 1 , 2 , 3

D − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 2

19 2 ( k – 3 ) 2 + 3 – 2k 2 =

A 21 – 8 kB 11k – 2C 12k – 2D 21 – 12k

y

xO

4

y

xO

4

y

xO

4

y

xO

4

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20 Express2

43

n

n

n

n

as a single fraction in its simplest form.

Ungkapkan2

43

n

n

n

n

sebagai pecahan tunggal dalam bentuk terendah.

An

n

4

3 2

Bn

nn

4

3 2

Cn

n

4

33

Dn

n

4

3 2

21 Given that 46

5

nm, then n =

Diberi 46

5

nm , maka n =

A ( 5 m – 24 )2

B 25 m + 24C 25 m 2 – 24

D 46

52

m

22 Given that 103)1(4 yy find the value of y.

Diberi bahawa 103)1(4 yy , carikan nilai y.

A 7B 5C 4D 2

2353

7x

can be written as

sebagaiditulisbolehx 53

7

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A 5

3

7 x

B 5

3

7x

C 521 x

D 521x

24 Simplify 42 53 hhh .

Permudahkan 42 53 hhh

A 88 h

B 78h

C 115 h

D 715h

25 List all the integers x that satisfy the inequalities xx 38 and 2183 xx

Senaraikan semua integer x yang memuaskan ketaksamaan xx 38 . dan 2183 xx

A 5,6,7,8

B 4,5,6,7

C ,1,0,1,2,3

D 3,4,5,6,7,8

26 The line graph in Diagram 12 shows the number of tourist who visit Melaka forperiod of 6 months .Graf garis dalam Rajah 12 menunjukkan bilangan pelancong yang melawat Melaka dalam tempoh 6bulan

Diagram 12Rajah 12

Month

0

Number of tourist

1000

Jun July Aug Sept Oct Nov

1500

2500

2000

500

3000

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The mode is

A JulyB AugustC SeptemberD November

27 Table 1 shows the cumulative frequency of scores obtained by a group of students ina certain games .Jadual 1 menunjukkan kekerapan longgokan skor yang diperolehi sekumpulan pelajar dalampermainan tertentu.

Score of studentsSkor pelajar

1 2 3 4 5 6

Cumulative frequencyKekerapan longgokan

3 10 p 28 40 42

Table 1Jadual 1

If the mode score is 3 , the minimum value of p isJika mod skor ialah 3 , nilai minimum bagi p ialah

A 12

B 13

C 15

D 23

28 Diagram 13 shows the graph of 2 nxay . What are the values of a and n ?.

Rajah 13 menunjukkan graf bagi suatu fungsi 2n

xay Apakah nilai-nilai bagi a dan n ?.

y

-1

2 nxay

x

2

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Diagram 13Rajah 13

A 2,2 na

B 2,2 na

C 3,2 na

D 3,2 na

29 Given that the universal set = { 3010: xx , x is an integer}.

Set P= { x : x is an even number}Set Q = { x : x is a number such that the sum of its digits is less than 5}List all the elements of set QP .

Diberi set semesta = { 3010: xx , x ialah integer}.

Set P = { x : x ialah nombor genap}Set Q = { x : x ialah nombor dengan keadaan hasil tambah digit-digitnya kurang daripada 5}

Senaraikan semua unsur bagi set QP .

A { 14, 16, 18, 24, 26, 28, 30 }

B { 16, 18, 24, 26, 28, 30 }

C { 10, 12, 20, 22, 30 }

D { 16, 18, 24, 26, 28 }

30 Diagram 14 is a Venn diagram showing the elements of the universal set, , set M andNRajah 14 ialah gambar rajah Venn yang menunjukkan unsur-unsur set semesta, , set M dan set N.

Which set represents the shaded region?Set manakah yang mewakili kawasan berlorek?

A NM

B NM

Diagram 14Rajah 14

NM

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C NM

D NM

31 Diagram 15 shows two straight lines, QR and RS, drawn on Cartesian plane. R lies onthe x-axis.Rajah 15 menunjukkan dua garis lurus, QR dan RS, dilukis di atas satah Cartesian. R terletak di ataspaksi-x

Given OR = 2OQ, find the gradient of RS.Diberi OR = 2OQ, cari kecerunan bagi RS.

A4

3

B3

4

C2

1

D2

1

32 Diagram 16 shows a straight line KL on a Cartesian plane.Rajah 16 menunjukkan garis lurus KL pada suatu satah Cartesan.

Find the value of h.Cari nilai h.

A2

5

xO

Q ( 0 , 3 )

S ( 9, 4 )

R

y

Diagram 15Rajah 15

y

x0

2x + 5y = 10

L ( h , 3 )

Diagram 16Rajah 16

K

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B5

2

C 2D 5

33 The coordinates of G is (0, 6) and the gradient of the straight line GH is3

2 . Find

the x- intercept of GH.

Koordinat bagi G ialah ( 0,6 ) dan kecerunan garis lurus GH ialah3

2 . Cari pintasan-x bagi RS.

A – 9

B – 1

C 4

D 9

34 A box contains 20 blue cards and some red cards. A card is chosen at random from

the box . The probability of choosing a blue card is7

5.

Find the number of red cards in the box .

Sebuah kotak mengandungi 20 keping kad biru dan beberapa keping kad merah . Sekeping kad

dipilih secara rawak daripada kotak itu .Kebarangkalian sekeping kad merah dipilih ialah7

5.

Cari bilangan kad merah dalam kotak itu .

A 8

B 15

C 28

D 35

35 Table 2 shows the distribution of a group of 120 students in two societies.Jadual 2 menunjukkan bilangan 120 murid dalam dua buah persatuan.

BoysLelaki

GirlsPerempuan

Mathematics SocietyPersatuan Matematik 35 20

English SocietyPersatuan B. Inggeris 40 25

Table 2Jadual 2

A student is chosen at random from the group to raise up the flag.What is the probability that a girl from the English society will be chosen ?Seorang murid dipilih secara rawak daripada kumpulan itu untuk menaikkan bendera.Apakah kebarangkalian seorang murid perempuan dari Persatuan Bahasa Inggeris akan dipilih ?

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A9

5

B13

5

C24

9

D24

5

36 A container holds 20 bars of chocolate with raisins and nuts. A bar of chocolate ispicked at random from the container. The probability of picking a bar of chocolate

with raisins is5

3.

How many bars of chocolate with nuts are there in the container ?Sebuah bekas mengandungi 20 bungkus coklat yang terdiri daripada coklat berkismis dan berkacang.Sebungkus coklat dipilih secara rawak daripada bekas itu. Kebarangkalian bahawa coklat itu

berkismis ialah5

3. Berapakah bilangan bungkus coklat berkacang dalam bekas itu?

A 2B 8C 12D 17

37 It is given that y αx

1and y = 4 when x = 9 . Calculate the value of y when x =

25 .

Diberi bahawa y αx

1dan y = 4 apabila x = 9. Hitungkan nilai y apabila x = 25

A5

12

B15

4

C12

1

D60

1

38 Table 3 shows two sets of values of p , q and r which satisfy r α pq .

Jadual 3 menunjukkan dua set bagi nilai p, q dan r yang memuaskan r α pq .

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p 2

1

3

1

q 6 w

r 45 25

Table 3Jadual 3

Calculate the value of w.Hitungkan nilai w.

A 5B 15C 45D 135

39

52

74+ 3

02

11

A

58

21

B

58

41

C

58

27

D

54

27

40 Calculate the values of m and of n in the following matrix equation .Carikan nilai-nilai bagi m dan n di dalam persamaan matrik berikut .

15

10m− 2

12

34=

n1

412

A m = − 1 , n = 3

B m = − 1 , n = 2

C m = − 4 , n = 3

D m = − 4 , n = 1

END OF QUESTION PAPER

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PEPERIKSAAN SELARAS PERTENGAHAN TAHUN

SIJIL PELAJARAN MALAYSIA 2010


MMAATTHHEEMMAATTIICCSSPPAAPPEERR 11 11444499//11

MMAATTHHEEMMAATTIICCSSPPAAPPEERR 11 11444499//11

MARKING SCHEME

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1 D 11 D 21 A 31 B

2 D 12 B 22 D 32 A

3 A 13 C 23 B 33 D

4 A 14 C 24 D 34 D

5 A 15 A 25 A 35 B

6 C 16 B 26 B 36 B

7 B 17 B 27 D 37 A

8 D 18 A 28 C 38 A

9 D 19 D 29 A 39 B

10 A 20 B 30 C 40 C

1449/2MathematicsPaper 2May2010

SEKOLAH MENENGAH SAINS MUZAFFAR SYAHAYER KEROH, 75450 MELAKA

NAME :………………………………………….……..

FORM: 4…………………

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PEPERIKSAAN AKHIR SEMESTER 12010

2. 2

Section Question Fullmark

Marksobtained

A

1 3

2 4

3 4

4 3

5 4

6 5

7 6

8 6

9 6

10 5

11 6

B

12 12

13 12

14 12

15 12

Total

MATHEMATICS

Paper 2Two hours and thirty minutes

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TODO SO

1. This question paper consist two section: Section A and Section B.Answer all questions in Section A and in Section B.

. Write your answers in the spaces provided in the question paper.

3. Working step must be written clearly.

4. Diagram given is not according to scale unless stated.

5. Marks for each question are given in bracket.

6. A list of formulae is given in pages 2 and 3.

8. Non programmable scientific calculator is allowed.

9 This question paper must be hand up at the end of the exam.

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This question paper consists of 21 printed pages.

SULIT 1449/1

1449/1 © 2010 Hak Cipta JPM [Lihat halaman sebelahSULIT

MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols given are theones commonly used..

RELATIONS

1nmnm aaa

2nmnm aaa

3mnnm aa )(

4

ac

bd

bcadA

11

5 Sn

AnAP

)()(

6 )(1)'( APAP

72

122

12 )()(Distance yyxx

8 Midpoint ,

2,

2),( 2121 yyxx

yx

9 Average speed =takentime

travelleddistance

10 Mean =dataofnumber

dataofsum

11 Meansfrequencieofsum

frequency)markof(classsum

12 Pythagoras Theorem222 bac

1312

12

xx

yym

14 erceptint

erceptint

x

ym

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24

SHAPES AND SPACE

1 Area of trapezium =2

1 sum of parallel sides height

2 Circumference of circle = rd 2

3 Area of circle = 2r

4 Curved surface area of cylinder = rh2

5 Surface area of sphere = 24 r

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = hr 2

8 Volume of cone = hr 2

3

1

9 Volume of sphere = 3

3

4r

10 Volume of right pyramid = 3

1base area height

11 Sum of interior angles of a polygon = (n – 2) 180º

12 o360

centeratsubtendedangle

circleofncecircumfere

lengtharc

13 o360


circleofarea

sectorofarea

14 Scale factor, k =PA

PA'

15 Area of image = k2 area of object

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25

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26

Section A[52 marks ]

Answer all questions in this section.

1 On the graph in the answer space, shade the region which satisfy the three inequalitiesy ≥ x , x ≥ 2 and y < 5 [3 marks ]

Pada graf yang disediakan di ruangan jawapan , lorekkan rantau yang memuaskan ketiga-tiga

ketaksamaan :y ≥ x , x ≥ 2 and y < 5

Answer :

2 Calculate the value of p and of q that satisfy the following simultaneous linearequations:Hitung nilai p dan nilai q yang memuaskan persamaan linear serentak berikut :

524

1 qp

84 qp [4 marks]

Answer :

y = x

x = 2

0

1

2

3

4

5

6

y

1 2 3 4 x

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27

3 Solve the quadratic equation:Selesaikan persamaan kuadratik berikut:

x

xx

)4(23

[ 4 marks]

Answer :

4 Diagram 4 shows a cuboid with TUVW as the horizontal base . L, M and N are themidpoints of PS, QR and UV respectively.Rajah 4 menunjukkan sebuah kuboid dengan tapak mengufuk TUVW. L, M dan N adalah titik tengahbagi PS, QR dan UV masing-masing.

Given WT = 8 cm, WV= 12 cm and QU = 4 cm.Identify and calculate the angle between the plane LVU and the plane QRVU.

[3 marks]Diberi WT = 8 cm, WV= 12 cm dan QU = 4 cm.Kenal pasti dan hitungkan sudut di antara satah LVU dengan satah QRVU.

Answer :

Diagram 4Rajah 4

Q

S

P

TU

VW

L M

NR

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28

5 Diagram 5 shows a solid in the shape of a right pyramid. V is vertically above the squarebase JKLM. A cylinder with radius 3 cm and height 6 cm is taken out of the solid.Rajah 5 menunjukkan sebuah pepejal berbentuk sebuah piramid tegak. V terletak tegak di atas tapak segiempat sama JKLM. Sebuah silinder yang berjejari 3 cm dan tinggi 6 cm dikeluarkan daripada pepejal itu.

Given JK = 8 cm and the height of the pyramid is 12 cm, calculate the volume, in cm3,of the remaining solid. ( Use = 3.142 ) [4 marks]Diberi JK = 8 cm dan tinggi piramid ialah 12 cm, hitungkan isipadu, dalam cm3, pepejal yang tinggal itu.

( Guna = 3.142 )

Answer :

J K

LM

V

Diagram 5Jadual 5

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29

6 In Diagram 6, O is the origin. Straight line SR is parallel to straight line PQ. The equation

of straight line SR is 24

3 xy .

Dalam Rajah 6 , O ialah asalan. Garis lurus SR adalah selari dengan garis lurus PQ. Persamaan garis

lurus SR ialah 24

3 xy .

FindCari

a) the coordinates of point Rkoordinat titik R

b) the equation of the straight line PQpersamaan garis lurus PQ.

[ 5 marks ]Answer:

(a)

R

Diagram 6Rajah 6

x

P

S

O

y Q ( 8 , 9 )

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30

(b)

7 Diagram 7 shows sector MPQ, sector MST and semicircle PQR with centre M.Rajah 7 menunjukkan sebuah sektor MPQ, sektor MST dan semibulatan PQR berpusat di M.

Given that PS =3PM, MQ = 7 cm and QMR = 120o. Using =7

22, calculate

Diberi bahawa PS = 3PM, MQ = 7 cm dan QMR = 120o. Dengan menggunakan =7

22, hitung

(a) the perimeter, in cm, of the whole diagramperimeter, dalam cm, seluruh rajah.

(b) the area, in cm2, of the shaded regionluas, dalam cm2, kawasan berlorek

[6 marks]

Answer:

(a)

S

T

P

Q

M R

Diagram 7Rajah 7

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31

(b)

8 (a) Inverse matrix of

24

31is

14

31 n

m.

Matriks songsang bagi

24

31 ialah

14

31 n

m.

Find the value of m and of n.Cari nilai m dan nilai n.

(b) Using matrices, calculate the value of x and of y that satisfy the followingsimultaneous linear equations:Menggunakan kaedah matrik, hitung nilai x dan nilai y yang memuaskan persamaan linearserentak berikut:

x – 3y = 5

4x – 2y = 10 [ 6 marks ]

Answer :

(a)

(b)

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32

9 (a) State three inequalities which satisfy the shaded region below.Nyatakan tiga ketaksamaan yang memenuhi rantau berlorek di bawah.

[3 marks]

Answer:

(a) ( i) ………………………………………..

(ii) …………………………………………

(iii) ……………………………………….

(b) The Venn diagrams in the answer space show set A, set B and set C, such that

the universal set CBA .Gambar rajah Venn di ruang jawapan menunjukkan set A, set B dan set C dengan keadaan set

semesta CBA .

y

x0

y = 2 x + 1

2y = x – 4

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33

On the diagrams in the answer space, shade the set [3 marks]Pada rajah di ruang jawapan, lorek set

(i) A B '(ii) CBA )(

Answer:

(i)

(ii)

10 (a) Diagram 10 shows thirteen labeled cards which are placed in a box .Rajah 10 menunjukkan tigabelas kad berlabel yang dimasukkan ke dalam sebuah kotak.

A car d is chosen at random from a box. By listing the possible outcomes of theevent , find the probability thatSatu kad dipilih secara rawak dari kotak itu. Dengan menyenaraikan semua kesudahan yangmungkin, cari kebarangkalian bahawa

(i) the card labeled with vowel are chosen.kad berlabel dengan vokal dipilih

(ii) the card labeled with R is chosen.kad berlabel R dipilih.

(b) Table 10 shows the marks scored by 140 students in a Mathematics tests.Jadual 10 menunjukkan markah yang di perolehi oleh 140 murid dalam ujian Matematik.

Marks Number of Students51 – 55 1156 – 60 4561 – 65 67

Diagram 10Rajah 10

P PE R E CI LDN U A R

A

B C

A

B C

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34

66 – 70 17

A students is selected at random from the group.Seorang murid dipilih secara rawak daripada kumpulan itu.

Find the probability that the mark is :Cari kebarangkalian bahawa markahnya ialah:

(i) in the class interval 61 – 65dalam selang kelas 61 – 65

(ii) less than 61 marks.kurang dari 61

[ 5 marks]Answer:

(a)

(i)

(ii)

(b) (i)

(ii)

11 (a) Complete the statement below using the quantifier “all” or “some” to form a true

statement.

Lengkapkan pernyataan berikut dengan menggunakan pengkuantiti “semua” atau “sebilangan”, untuk

membentuk suatu pernyataan yang benar.

(b) Co

Le

Pr

Pre

Pr

Jadual 10

…………… quadratic equations have different roots.

10 Hak Cipta JPM

mplete the premise in the follow

ngkapkan premis dalam hujah berikut:

emise 1 : If set P

mis 1 : Jika set

emise 2 / Premis 2 : ………

…………… persamaan kuadratik m

Table 10

[Lihat halaman sebelahSULIT

ing argument:

is a subset of set Q , then PQP .

P adalah subset bagi set Q , maka PQP .

………………………………………………………….

empunyai punca - punca yang berlainan.

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1449/1 © 2010 Hak Cipta JPM

35

Conclusion : Set P is not a subset of set Q.

Kesimpulan : Set P bukan subset bagi set Q.

(c) Write down two implications based on the following sentence.

Tuliskan dua impikasi berdasarkan ayat di bawah.

(d) Make a general co

follows the pattern

Buat satu kesimpulan

Answer:

(a) ……………………

(b) Premise 2 : ………

(c) Implication 1 : ……

Implication 2 : ……

(d) ………………………

x3 = 125 if and only is x = 53


nclusion by induction for the number sequence 2, 10, 24, ... which

:

umum secara aruhan bagi urutan nombor 2, 10, 24, .. yang mengikut pola berikut :

7 = 3(2)1 + 1

14 = 3(2)2 + 2

27= 3(2)3 + 3

... = ........... [6 marks]

………………………………………………………………………

……………………………………………………………….............

……………………………………………………………………….

…………………………………………………………………...….

………………………………………………………………….…

Section B

[48 marks]

x = 125 jika dan hanya jika x = 5

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36

Answer all questions from this section.

12. (a) Table 12 in the answer space shows the values of x and of y for the equation

xy

4 .

Find the value of p and of q. [2 marks]

Jadual 12 di ruang jawapan menunjukkan nilai – nilai x dan y bagi persamaanx

y4

.

Cari nilai bagi p dan q.

(b) For this part of the question, use the graph provided on page 15. You may use aflexible curve rule.

Untuk ceraian soalan ini, gunakan kertas graf yang disediakan pada halaman 15. Anda bolehmenggunakan pembaris fleksible.

By using a scale of 2 cm to 1 unit on the both axes, draw the graph ofx

y4

for

65.0 x .

Dengan menggunakan skala 2 cm kepada 1 unit pada kedua – dua paksi , lukis graf bagi fungsi

xy

4 untuk 65.0 x . [4 marks]

(c) Using the graph drawn in 12(b), findMenggunakan graf yang dilukis di 12(b) , carikan

(i) the value of x when y = 5.4nilai x apabila y = 5.4

(ii) the value of y when x = 4.5nilai y apabila x = 4.5 [2 marks]

(d) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation 427 2 xx for 65.0 x .

State these values of x [4 marks]Lukiskan satu garis lurus yang sesuai pada graf anda untuk mencari nilai – nilai x yang

memuaskan persamaan 427 2 xx bagi 65.0 x .

Nyatakan nilai-nilai x tersebut .

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37

Answer :

(a)

x 0.5 1 1.5 2 2.5 3 4 5 6

y 8 4 2.67 2 p 1.33 1 q 0.67

Table 12Jadual 12

p = ………………………

q = ………………………

(b) Refer graph on page 15.

(c) (i) x = ……………………….

(ii) y = ………………………..

(d) x = ………………………. , ……………………….

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Graph for Question 12

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39

13 (a) Transformation T is a translation

2

3and transformation P is an anticlockwise

rotation of 90° about the centre ( 1 , 2 ).

Penjelmaan T ialah translasi

2

3dan penjelmaan P ialah putaran 90° ikut arah lawan jam pada

pusat ( 1, 2 ).

State the coordinates of the image of point ( 0 , 6 ) under each of the following

transformations:

Nyatakan koordinat imej bagi titik ( 0, 6 ) di bawah setiap penjelmaan berikut:

(i) P,

(ii) PT,

(iii) T 2. [5 marks]

(b) Diagram 13 shows three quadrilaterals, ABCD, EFGH and JKLM, drawn on aCartesian plane.

Rajah 13 menunjukkan tiga sisiempat, ABCD, EFGH dan JKLM, dilukis pada suatu satah Cartesan.

–2–4 42O

2

4

6

8K

A

B

D

C

–6

y

E

F

J

Diagram 13Rajah 13


86x

MHG

L

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40

(i) JKLM is the image of ABCD under the combined transformation VU.Describe in full the transformations:

JKLM ialah imej bagi ABCD di bawah gabungan penjelmaan VU.

Huraikan selengkapnya:

(a) U,

(b) V.

(ii) It is given that quadrilateral ABCD represents a region of area 32 cm2.

Calculate the area ,in cm2, of the region represented by the shaded region

Diberi bahawa sisiempat ABCD mewakili suatu kawasan yang mempunyai keluasan 32 cm2.

Hitungkan luas, dalam cm2, kawasan yang diwakili oleh rantau berlorek.

[7 marks]

Answer :

(a) (i)

(ii)

(iii)

(b) (i) U :………………………………………………………………………...

…………………………………………………………………………

(ii) V : ……………………………………………………………………….....

SULIT 1449/1


41

…………………………………………………………………………..

(c)

14 The data in Diagram 14 shows the body weight, in kg, of 32 children in a kindergarten.Data dalam Rajah 14 menunjukkan timbangan berat , dalam kg, bagi 32 murid dalam sebuah tadika.

a) Based on the data in Diagram 14 and by using the class interval of 3, completeTable 14 in the answer space..Berdasarkan data dalam Rajah 14 dan dengan menggunakan selang kelas 3, lengkapkan Jadual14 di ruangan jawapan..

28 11 23 27 20 15 30 24

27 25 17 19 16 23 25 26

29 17 23 12 20 21 23 28

29 19 33 24 23 24 25 31

Diagram 14Rajah 14

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42

b) Based on Table 14 in (a), calculate the mean weight, in kg.Berdasarkan Jadual 14 di (a), hitungkan min berat, dalam kg.

c) By using a scale of 2 cm to 3 kg on the horizontal axis and 2 cm to 1 child on thevertical axis, draw a histogram for the data.Dengan menggunakan skala 2 cm kepada 3 kg pada paksi mengufuk dan 2 cm kepada 1 muridpada paksi mencancang, lukiskan satu histogram bagi data tersebut

(d) State one information obtained based on the histogram in 14(c).Nyatakan satu maklumat berdasarkan histogram di 14(c)

Answer :(a)

Class interval Frequency Midpoint

10 – 12

.

Table 14Jadual 14

(b)

(d) ..........................................................................................................................................

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44

15 (a) Given that m varies directly as the cube of n and m = 36 when n = 2, expressm in term of n . Hence, find the positive value of n when m = 288.

Diberi bahawa m berubah secara langsung dengan kuasa tiga n dan m = 36 apabila n = 2,ungkapkan m dalam sebutan n. Seterusnya carikan nilai n apabila m = 288.

[3 marks]

(b) Table 15 shows the relation between three variables, p , q and r.Jadual 15 menunjukkan hubungan antara tiga pembolehubah p, q dan r.

p q r

3 6 2

8 25 y

6 w 3

Table 15Jadual 15

Given that2r

qp , calculate the values of w and of y.

Diberi bahawa2r

qp , hitungkan nilai-nilai w dan y. [5 marks]

(c) In Diagram 15, QRS is a straight line.Dalam Rajah 15, QRS adalah garis lurus.

FindCari

(i) the value of θcos ?nilai θkos

(ii) PRS [4 marks]

Q P

R

S

3 cm

4 cm

oθ

Diagram 15Rajah 15

SULIT 1449/1


45

Answer :

(a)

(b)

(c) (i)

(ii)

END OF QUESTION PAPER

SULIT 1449/1


46



MMAATTEEMMAATTIIKKKKEERRTTAASS 22 11444499//22

JAWAPAN

SULIT 1449/1

1449/1 © 2010 H

47

No

1

2

3

4

ak Cipta JPM [Lihat halaman sebelahSULIT

MARKAH MAKSIMUM BAGI KERTAS INI : 100 MARKAH

Peraturan Pemarkahan Markah

Line y = 5

Correctly shaded

1

2

3

p + 8q = 20 @ equivalent−4q = −12 @ equivalent

q = 3p = − 4

1111

4

3x2 – 2x – 8 = 0(3x + 4) ( x – 2) = 0

2,3

4 xx

11

1,14

LNM

tan =4

12

= 71.57◦ or 71o 34'

12

14

MATHEMATICS 1449 / 2

y = x

x = 2

0

1

2

3

4

5

6

y

1 2 3 4 x

SULIT 1449/1


48

No Peraturan Pemarkahan Markah

5 1288142.33

1

633142.3

633142.31288142.33

1

86.33

1

111

4

6 (a) 24

310 x

3

8x

(b) m =4

3

c )8(4

39 or c = 3

34

3 xy

1

1

1

1

1 5

7(a) 14

7

222

360

120 @ 7

7

222

360

60

147

222

360

120 + 7

7

222

360

60 + 21 + 14

3

215@

3

271 @ 71.67

(b) 2147

22

360

120 , atau @ equivalent

( 2147

22

360

120 ─ 27

7

22

360

120 ) + 27

7

22

360

60 @ equivalent

3

539@

3

2179 @ 179.67

1

1

1

1

1

16

8(a) m = 10, n = 2

Note :

14

31 n

m=

14

32

4)3()2(1

1award 1 mark

(b)

10

5

24

31

y

x

10

5

14

32

)43)2(1(

1

y

x

x = 2 y = ─1

1,1

1

1

1, 1 6

SULIT 1449/1


49


9 (a) 42 xy

12 xy

1y

(b) (i)

(ii)

111

1

2

6

10 (a) {P, E, R, N, D, I, C, U, L, A, R}

(i)13

5

(ii)13

2

(b) (i)140

67

(ii)140

56or

5

2

1

1

1

1

15

11(a) Some

(b) PQP

(c) If x3 = 125, then x = 5If x = 5, then x3 = 125

(d) 3n2─ n ; n = 1,2,3,4, …

Note : 1 + 2n2 only award 1 mark

1

1

11

1, 16

A

B C

A

B C

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50


12 (a) p = 1.6 , q = 0.8

(b) Refer to graphUniform scale and correct axisPlot all points correctlySmooth curve

(c) (i) x = 0.8 ± 0.1(ii) y = 0.9 ± 0.1

(d) y = 2x 7 @ 2x 7 =x

4

Draw line y = 2x 7x = 2.7 ± 0.1, 0.7 ± 0.1

1 ,1

121

11

11

1,112

13 (a) (i) (3, 7)(ii) (6 , 5)(iii) (12 , 4)

(b) (i) (a) U : Reflection , x = 1.Note : Reflection only award 1 mark

(b) W : Enlargement with scale factor = 3 ,at centre (5 , 4)

Note : 1. Enlargement with scale factor = 3 only @ Enlargement atcentre (5 , 4) award 2 marks

2. Enlargement only award 1 mark

(ii) 32 3232 32 32256

122

2

3

111

12

14(a)

Classinterval

Frequency Midpoint

10 – 12 2 1113 – 15 1 1416 – 18 3 1719 – 21 5 2022 – 24 8 2325 – 27 6 2628 – 30 5 29

1, 2, 1

SULIT 1449/1


51


31 – 33 2 32

(b)32

)32(2)29(5)26(6)23(8)20(5)17(3)14(1)11(2

23

(c) Refer to graphUniform scale and correct axis,Eight bars correctly drawn..Using upper boundary or class interval or midpoint as x – axis

(d) Any correct information from the histogram.

2

1

121

112

15 (a) 36 = k (2)3 or2

9k

3

2

9288 n

n = 4

(b) k = 2

(i)2

)25(28

y

y = 2

5

(ii)23

26

w

w = 27

(c) (i) RP = 5

5

3RPQcos

cos =5

3

(ii) θ = 126.87o

1

11

1

1

1

11

1

11

112

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52Graph for Question 12y

1

0 4321 5 6x

−7

−6

x

x

x

x

xx

x

x

−1

−2

−3

−4

−5

−8

x

SULIT 1449/1


53

1

2

3

4

5

6

7

8

9


0 11 14 17 20 23 26 29 32

Documents

MATHS SPM PAPER 1 QUESTIONS - api.ning.comapi.ning.com/files/4aPiF8TWV1mSnnT4gyjRPWwQAh2Fh5Xhze5CQsUb*B1x4X…3. Each question is followed by four choices of answers A, B, C and D